# Arcsuperfac.cin

// Arcsuperfac.cin is algorithm to evaluate the inverse function for Superfac.cin. // The algorithm below evaluates the AbelFunction of Factorial. //This algorithm is used to make pictures in publication [1].

//Later, the SuperFactorial and AbelFactorial had been redefined in order to have SuperFactorial(0)=3 and AbelFactorial(3)=0.

## Code

```z_type arcsuperfac0(z_type z){ int n; z_type s, c, e;
DB k=0.61278745233070836381366079016859252;
DB U[19]={1.,                           -0.798731835172434541585621072345730147,
0.69806411355936704552792746483306691,  -0.6339640557572814865638000833478131,
0.5884152357911398848274232132172143,   -0.5538887519936519511632593654732843,
0.526547902598592454703287733600892,    -0.504191460428021561516069870422848,
0.48545298002933922263549078734881,     -0.46943468090947139273094056497701,
0.4555204862393622788179080677150,      -0.4432726222110411295132308010077,
0.4323708863150174727399798603985,      -0.4225752531177612936293974175008,
0.413701949171132722406449918702,       -0.40560764595293667778491699902,
0.39817872478532299454624349817,        -0.391323       -0.384};
//      z-=2.; s=U[15]*z; for(n=14;n>=0;n--){ s+=U[n]; s*=z;}
z-=2.; s=U[18]*z; for(n=17;n>=0;n--){ s+=U[n]; s*=z;}
return log(s)/k;}
z_type arcsuperfac(z_type z){ if(abs(z-2.)<.12) return arcsuperfac0(z);
return  arcsuperfac(afacc(z))+1.;}
```

## Out of date

Name arcsuperfac is too long. Therefore, the routine AuFac.cin that does the same is loaded.